Question: Solve for $x$ and $y$ using elimination. ${2x+3y = 17}$ ${-2x-2y = -12}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {2x+3y = 17}\thinspace$ to find $x$ ${2x + 3}{(5)}{= 17}$ $2x+15 = 17$ $2x+15{-15} = 17{-15}$ $2x = 2$ $\dfrac{2x}{{2}} = \dfrac{2}{{2}}$ ${x = 1}$ You can also plug ${y = 5}$ into $\thinspace {-2x-2y = -12}\thinspace$ and get the same answer for $x$ : ${-2x - 2}{(5)}{= -12}$ ${x = 1}$